We offer a systematic study of rigid analytic motives over general rigid analytic spaces, and we develop their six-functor formalism. A key ingredient is an extended proper base change theorem that we are able to justify by reducing to the case of algebraic motives. In fact, more generally, we develop a powerful technique for reducing questions about rigid analytic motives to questions about algebraic motives, which is likely to be useful in other contexts as well. We pay special attention to establishing our results without noetherianity assumptions on rigid analytic spaces. This is indeed possible using Raynaud's approach to rigid analytic geometry.

The six-functor formalism for rigid analytic motives / J. Ayoub, M. Gallauer, A. Vezzani. - In: FORUM OF MATHEMATICS. SIGMA. - ISSN 2050-5094. - 10:(2022 Aug 08), pp. e61.1-e61.182. [10.1017/fms.2022.55]

The six-functor formalism for rigid analytic motives

A. Vezzani
Co-primo
2022

Abstract

We offer a systematic study of rigid analytic motives over general rigid analytic spaces, and we develop their six-functor formalism. A key ingredient is an extended proper base change theorem that we are able to justify by reducing to the case of algebraic motives. In fact, more generally, we develop a powerful technique for reducing questions about rigid analytic motives to questions about algebraic motives, which is likely to be useful in other contexts as well. We pay special attention to establishing our results without noetherianity assumptions on rigid analytic spaces. This is indeed possible using Raynaud's approach to rigid analytic geometry.
Settore MAT/02 - Algebra
Settore MAT/03 - Geometria
Article (author)
File in questo prodotto:
File Dimensione Formato  
the-six-functor-formalism-for-rigid-analytic-motives.pdf

accesso aperto

Tipologia: Publisher's version/PDF
Dimensione 2.2 MB
Formato Adobe PDF
2.2 MB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/808282
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact